Preheat the oven to 425 degrees F (220 degrees C).
In a medium bowl, stir together the sour cream, white sugar, 1/3 cup flour and almond extract until smooth. Sprinkle 1 tablespoon of flour over the pie crust to prevent it from getting soggy. Alternate layers of peaches and the sour cream mixture, beginning with a layer of peaches and ending with a layer of sour cream.
Bake for 20 minutes in the preheated oven. Reduce the heat to 350 degrees F (175 degrees C). Continue baking for an additional 35 minutes. Remove the pie from the oven and sprinkle brown sugar over the top. Set the oven to Broil, and broil for 2 to 3 minutes, until caramelized.